System constraints method of controlling operation of an electro-mechanical transmission with two external input torque ranges

ABSTRACT

A method to control an electro-mechanical transmission mechanically-operatively coupled to an internal combustion engine and first and second electric machines to transmit power to an output member includes determining motor torque constraints and battery power constraints. A preferred output torque to an output member is determined that is achievable within the motor torque constraints and is achievable within a range for a first torque input and is achievable within a range for a second torque input and is based upon the battery power constraints.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional Application No.60/984,830 filed on Nov. 2, 2007 which is hereby incorporated herein byreference.

TECHNICAL FIELD

This disclosure pertains to control systems for electro-mechanicaltransmissions.

BACKGROUND

The statements in this section merely provide background informationrelated to the present disclosure and may not constitute prior art.

Known hybrid powertrain architectures can include multipletorque-generative devices, including internal combustion engines andnon-combustion machines, e.g., electric machines, which transmit torquethrough a transmission device to an output member. One exemplary hybridpowertrain includes a two-mode, compound-split, electro-mechanicaltransmission which utilizes an input member for receiving tractivetorque from a prime mover power source, preferably an internalcombustion engine, and an output member. The output member can beoperatively connected to a driveline for a motor vehicle fortransmitting tractive torque thereto. Machines, operative as motors orgenerators, can generate torque inputs to the transmission independentlyof a torque input from the internal combustion engine. The machines maytransform vehicle kinetic energy transmitted through the vehicledriveline to energy that is storable in an energy storage device. Acontrol system monitors various inputs from the vehicle and the operatorand provides operational control of the hybrid powertrain, includingcontrolling transmission operating state and gear shifting, controllingthe torque-generative devices, and regulating the power interchangeamong the energy storage device and the machines to manage outputs ofthe transmission, including torque and rotational speed.

SUMMARY

A powertrain includes an electro-mechanical transmissionmechanically-operatively coupled to an internal combustion engine andfirst and second electric machines to transmit power to an outputmember. A method for controlling the electro-mechanical transmissionincludes determining motor torque constraints for the first and secondelectric machines, and determining battery power constraints for anelectrical energy storage device electrically connected to the first andsecond electric machines. A range for a first torque input to theelectro-mechanical transmission is determined and a range for a secondtorque input to the electro-mechanical transmission is determined. Apreferred output torque to the output member of the electro-mechanicaltransmission is determined that is achievable within the motor torqueconstraints, is achievable within the range for the first torque input,is achievable within the range for the second torque input, and is basedupon the battery power constraints.

BRIEF DESCRIPTION OF THE DRAWINGS

One or more embodiments will now be described, by way of example, withreference to the accompanying drawings, in which:

FIG. 1 is a schematic diagram of an exemplary powertrain, in accordancewith the present disclosure;

FIG. 2 is a schematic diagram of an exemplary architecture for a controlsystem and powertrain, in accordance with the present disclosure; and

FIGS. 3, 4, 5 (including 5A and 5B) are graphical diagrams, inaccordance with the present disclosure.

DETAILED DESCRIPTION

Referring now to the drawings, wherein the showings are for the purposeof illustrating certain exemplary embodiments only and not for thepurpose of limiting the same, FIGS. 1 and 2 depict an exemplaryelectro-mechanical hybrid powertrain. The exemplary electro-mechanicalhybrid powertrain in accordance with the present disclosure is depictedin FIG. 1, comprising a two-mode, compound-split, electro-mechanicalhybrid transmission 10 operatively connected to an engine 14 and firstand second electric machines (‘MG-A’) 56 and (‘MG-B’) 72. The engine 14and first and second electric machines 56 and 72 each generate powerwhich can be transferred to the transmission 10. The power generated bythe engine 14 and the first and second electric machines 56 and 72 andtransferred to the transmission 10 is described in terms of input andmotor torques, referred to herein as T_(I), T_(A), and T_(B)respectively, and speed, referred to herein as N_(I), N_(A), and N_(B),respectively.

The exemplary engine 14 comprises a multi-cylinder internal combustionengine selectively operative in several states to transfer torque to thetransmission 10 via an input shaft 12, and can be either aspark-ignition or a compression-ignition engine. The engine 14 includesa crankshaft (not shown) operatively coupled to the input shaft 12 ofthe transmission 10. A rotational speed sensor 11 monitors rotationalspeed of the input shaft 12. Power output from the engine 14, comprisingrotational speed and engine torque, can differ from the input speedN_(I) and the input torque T_(I) to the transmission 10 due to placementof torque-consuming components on the input shaft 12 between the engine14 and the transmission 10, e.g., a hydraulic pump (not shown) and/or atorque management device (not shown).

The exemplary transmission 10 comprises three planetary-gear sets 24, 26and 28, and four selectively engageable torque-transferring devices,i.e., clutches C1 70, C2 62, C3 73, and C4 75. As used herein, clutchesrefer to any type of friction torque transfer device including single orcompound plate clutches or packs, band clutches, and brakes, forexample. A hydraulic control circuit 42, preferably controlled by atransmission control module (hereafter ‘TCM’) 17, is operative tocontrol clutch states. Clutches C2 62 and C4 75 preferably comprisehydraulically-applied rotating friction clutches. Clutches C1 70 and C373 preferably comprise hydraulically-controlled stationary devices thatcan be selectively grounded to a transmission case 68. Each of theclutches C1 70, C2 62, C3 73, and C4 75 is preferably hydraulicallyapplied, selectively receiving pressurized hydraulic fluid via thehydraulic control circuit 42.

The first and second electric machines 56 and 72 preferably comprisethree-phase AC machines, each including a stator (not shown) and a rotor(not shown), and respective resolvers 80 and 82. The motor stator foreach machine is grounded to an outer portion of the transmission case68, and includes a stator core with coiled electrical windings extendingtherefrom. The rotor for the first electric machine 56 is supported on ahub plate gear that is operatively attached to shaft 60 via the secondplanetary gear set 26. The rotor for the second electric machine 72 isfixedly attached to a sleeve shaft hub 66.

Each of the resolvers 80 and 82 preferably comprises a variablereluctance device including a resolver stator (not shown) and a resolverrotor (not shown). The resolvers 80 and 82 are appropriately positionedand assembled on respective ones of the first and second electricmachines 56 and 72. Stators of respective ones of the resolvers 80 and82 are operatively connected to one of the stators for the first andsecond electric machines 56 and 72. The resolver rotors are operativelyconnected to the rotor for the corresponding first and second electricmachines 56 and 72. Each of the resolvers 80 and 82 is signally andoperatively connected to a transmission power inverter control module(hereafter ‘TPIM’) 19, and each senses and monitors rotational positionof the resolver rotor relative to the resolver stator, thus monitoringrotational position of respective ones of first and second electricmachines 56 and 72. Additionally, the signals output from the resolvers80 and 82 are interpreted to provide the rotational speeds for first andsecond electric machines 56 and 72, i.e., N_(A) and N_(B), respectively.

The transmission 10 includes an output member 64, e.g. a shaft, which isoperably connected to a driveline 90 for a vehicle (not shown), toprovide output power to the driveline 90 that is transferred to vehiclewheels 93, one of which is shown in FIG. 1. The output power at theoutput member 64 is characterized in terms of an output rotational speedN_(O) and an output torque T_(O). A transmission output speed sensor 84monitors rotational speed and rotational direction of the output member64. Each of the vehicle wheels 93 is preferably equipped with a sensor94 adapted to monitor wheel speed, the output of which is monitored by acontrol module of a distributed control module system described withrespect to FIG. 2, to determine vehicle speed, and absolute and relativewheel speeds for braking control, traction control, and vehicleacceleration management.

The input torque from the engine 14 and the motor torques from the firstand second electric machines 56 and 72 (T_(I), T_(A), and T_(B)respectively) are generated as a result of energy conversion from fuelor electrical potential stored in an electrical energy storage device(hereafter ‘ESD’) 74. The ESD 74 is high voltage DC-coupled to the TPIM19 via DC transfer conductors 27. The transfer conductors 27 include acontactor switch 38. When the contactor switch 38 is closed, undernormal operation, electric current can flow between the ESD 74 and theTPIM 19. When the contactor switch 38 is opened electric current flowbetween the ESD 74 and the TPIM 19 is interrupted. The TPIM 19 transmitselectrical power to and from the first electric machine 56 by transferconductors 29, and the TPIM 19 similarly transmits electrical power toand from the second electric machine 72 by transfer conductors 31 tomeet the torque commands for the first and second electric machines 56and 72 in response to the motor torques T_(A) and T_(B). Electricalcurrent is transmitted to and from the ESD 74 in accordance with whetherthe ESD 74 is being charged or discharged.

The TPIM 19 includes the pair of power inverters (not shown) andrespective motor control modules (not shown) configured to receive thetorque commands and control inverter states therefrom for providingmotor drive or regeneration functionality to meet the commanded motortorques T_(A) and T_(B). The power inverters comprise knowncomplementary three-phase power electronics devices, and each includes aplurality of insulated gate bipolar transistors (not shown) forconverting DC power from the ESD 74 to AC power for powering respectiveones of the first and second electric machines 56 and 72, by switchingat high frequencies. The insulated gate bipolar transistors form aswitch mode power supply configured to receive control commands. Thereis typically one pair of insulated gate bipolar transistors for eachphase of each of the three-phase electric machines. States of theinsulated gate bipolar transistors are controlled to provide motor drivemechanical power generation or electric power regenerationfunctionality. The three-phase inverters receive or supply DC electricpower via DC transfer conductors 27 and transform it to or fromthree-phase AC power, which is conducted to or from the first and secondelectric machines 56 and 72 for operation as motors or generators viatransfer conductors 29 and 31 respectively.

FIG. 2 is a schematic block diagram of the distributed control modulesystem. The elements described hereinafter comprise a subset of anoverall vehicle control architecture, and provide coordinated systemcontrol of the exemplary hybrid powertrain described in FIG. 1. Thedistributed control module system synthesizes pertinent information andinputs, and executes algorithms to control various actuators to meetcontrol objectives, including objectives related to fuel economy,emissions, performance, drivability, and protection of hardware,including batteries of ESD 74 and the first and second electric machines56 and 72. The distributed control module system includes an enginecontrol module (hereafter ‘ECM’) 23, the TCM 17, a battery pack controlmodule (hereafter ‘BPCM’) 21, and the TPIM 19. A hybrid control module(hereafter ‘HCP’) 5 provides supervisory control and coordination of theECM 23, the TCM 17, the BPCM 21, and the TPIM 19. A user interface(‘UI’) 13 is signally connected to a plurality of devices through whicha vehicle operator controls or directs operation of theelectro-mechanical hybrid powertrain. The devices include an acceleratorpedal 113 (‘AP’), an operator brake pedal 112 (‘BP’), a transmissiongear selector 114 (‘PRNDL’), and a vehicle speed cruise control (notshown). The transmission gear selector 114 may have a discrete number ofoperator-selectable positions, including the rotational direction of theoutput member 64 to enable one of a forward and a reverse direction.

The aforementioned control modules communicate with other controlmodules, sensors, and actuators via a local area network (hereafter‘LAN’) bus 6. The LAN bus 6 allows for structured communication ofstates of operating parameters and actuator command signals between thevarious control modules. The specific communication protocol utilized isapplication-specific. The LAN bus 6 and appropriate protocols providefor robust messaging and multi-control module interfacing between theaforementioned control modules, and other control modules providingfunctionality including e.g., antilock braking, traction control, andvehicle stability. Multiple communications buses may be used to improvecommunications speed and provide some level of signal redundancy andintegrity. Communication between individual control modules can also beeffected using a direct link, e.g., a serial peripheral interface(‘SPI’) bus (not shown).

The HCP 5 provides supervisory control of the hybrid powertrain, servingto coordinate operation of the ECM 23, TCM 17, TPIM 19, and BPCM 21.Based upon various input signals from the user interface 13 and thehybrid powertrain, including the ESD 74, the HCP 5 determines anoperator torque request, an output torque command, an engine inputtorque command, clutch torque(s) for the applied torque-transferclutches C1 70, C2 62, C3 73, C4 75 of the transmission 10, and themotor torques T_(A) and T_(B) for the first and second electric machines56 and 72. The TCM 17 is operatively connected to the hydraulic controlcircuit 42 and provides various functions including monitoring variouspressure sensing devices (not shown) and generating and communicatingcontrol signals to various solenoids (not shown) thereby controllingpressure switches and control valves contained within the hydrauliccontrol circuit 42.

The ECM 23 is operatively connected to the engine 14, and functions toacquire data from sensors and control actuators of the engine 14 over aplurality of discrete lines, shown for simplicity as an aggregatebi-directional interface cable 35. The ECM 23 receives the engine inputtorque command from the HCP 5. The ECM 23 determines the actual engineinput torque, T_(I), provided to the transmission 10 at that point intime based upon monitored engine speed and load, which is communicatedto the HCP 5. The ECM 23 monitors input from the rotational speed sensor11 to determine the engine input speed to the input shaft 12, whichtranslates to the transmission input speed, N_(I). The ECM 23 monitorsinputs from sensors (not shown) to determine states of other engineoperating parameters including, e.g., a manifold pressure, enginecoolant temperature, ambient air temperature, and ambient pressure. Theengine load can be determined, for example, from the manifold pressure,or alternatively, from monitoring operator input to the acceleratorpedal 113. The ECM 23 generates and communicates command signals tocontrol engine actuators, including, e.g., fuel injectors, ignitionmodules, and throttle control modules, none of which are shown.

The TCM 17 is operatively connected to the transmission 10 and monitorsinputs from sensors (not shown) to determine states of transmissionoperating parameters. The TCM 17 generates and communicates commandsignals to control the transmission 10, including controlling thehydraulic circuit 42. Inputs from the TCM 17 to the HCP 5 includeestimated clutch torques for each of the clutches, i.e., C1 70, C2 62,C3 73, and C4 75, and rotational output speed, N_(O), of the outputmember 64. Other actuators and sensors may be used to provide additionalinformation from the TCM 17 to the HCP 5 for control purposes. The TCM17 monitors inputs from pressure switches (not shown) and selectivelyactuates pressure control solenoids (not shown) and shift solenoids (notshown) of the hydraulic circuit 42 to selectively actuate the variousclutches C1 70, C2 62, C3 73, and C4 75 to achieve various transmissionoperating range states, as described hereinbelow.

The BPCM 21 is signally connected to sensors (not shown) to monitor theESD 74, including states of electrical current and voltage parameters,to provide information indicative of parametric states of the batteriesof the ESD 74 to the HCP 5. The parametric states of the batteriespreferably include battery state-of-charge, battery voltage, batterytemperature, and available battery power, referred to as a range P_(BAT)_(—) _(MIN) to P_(BAT) _(—) _(MAX).

A brake control module (hereafter ‘BrCM’) 22 is operatively connected tofriction brakes (not shown) on each of the vehicle wheels 93. The BrCM22 monitors the operator input to the brake pedal 112 and generatescontrol signals to control the friction brakes and sends a controlsignal to the HCP 5 to operate the first and second electric machines 56and 72 based thereon.

Each of the control modules ECM 23, TCM 17, TPIM 19, BPCM 21, and BrCM22 is preferably a general-purpose digital computer comprising amicroprocessor or central processing unit, storage mediums comprisingread only memory (‘ROM’), random access memory (‘RAM’), electricallyprogrammable read only memory (‘EPROM’), a high speed clock, analog todigital (‘A/D’) and digital to analog (‘D/A’) circuitry, andinput/output circuitry and devices (‘I/O’) and appropriate signalconditioning and buffer circuitry. Each of the control modules has a setof control algorithms, comprising resident program instructions andcalibrations stored in one of the storage mediums and executed toprovide the respective functions of each computer. Information transferbetween the control modules is preferably accomplished using the LAN bus6 and serial peripheral interface buses. The control algorithms areexecuted during preset loop cycles such that each algorithm is executedat least once each loop cycle. Algorithms stored in the non-volatilememory devices are executed by one of the central processing units tomonitor inputs from the sensing devices and execute control anddiagnostic routines to control operation of the actuators, using presetcalibrations. Loop cycles are executed at regular intervals, for exampleeach 3.125, 6.25, 12.5, 25 and 100 milliseconds during ongoing operationof the hybrid powertrain. Alternatively, algorithms may be executed inresponse to the occurrence of an event.

The exemplary hybrid powertrain selectively operates in one of severaloperating range states that can be described in terms of an engine statecomprising one of an engine-on state (‘ON’) and an engine-off state(‘OFF’), and a transmission state comprising a plurality of fixed gearsand continuously variable operating modes, described with reference toTable 1, below.

TABLE 1 Engine Transmission Operating Applied Description State RangeState Clutches M1_Eng_Off OFF EVT Mode 1 C1 70 M1_Eng_On ON EVT Mode 1C1 70 G1 ON Fixed Gear Ratio 1 C1 70 C4 75 G2 ON Fixed Gear Ratio 2 C170 C2 62 M2_Eng_Off OFF EVT Mode 2 C2 62 M2_Eng_On ON EVT Mode 2 C2 62G3 ON Fixed Gear Ratio 3 C2 62 C4 75 G4 ON Fixed Gear Ratio 4 C2 62 C373

Each of the transmission operating range states is described in thetable and indicates which of the specific clutches C1 70, C2 62, C3 73,and C4 75 are applied for each of the operating range states. A firstcontinuously variable mode, i.e., EVT Mode 1, or M1, is selected byapplying clutch C1 70 only in order to “ground” the outer gear member ofthe third planetary gear set 28. The engine state can be one of ON(‘M1_Eng_On’) or OFF (‘M1_Eng_Off’). A second continuously variablemode, i.e., EVT Mode 2, or M2, is selected by applying clutch C2 62 onlyto connect the shaft 60 to the carrier of the third planetary gear set28. The engine state can be one of ON (‘M2_Eng_On’) or OFF(‘M2_Eng_Off’). For purposes of this description, when the engine stateis OFF, the engine input speed is equal to zero revolutions per minute(‘RPM’), i.e., the engine crankshaft is not rotating. A fixed gearoperation provides a fixed ratio operation of input-to-output speed ofthe transmission 10, i.e., N_(I)/N_(O). A first fixed gear operation(‘G1’) is selected by applying clutches C1 70 and C4 75. A second fixedgear operation (‘G2’) is selected by applying clutches C1 70 and C2 62.A third fixed gear operation (‘G3’) is selected by applying clutches C262 and C4 75. A fourth fixed gear operation (‘G4’) is selected byapplying clutches C2 62 and C3 73. The fixed ratio operation ofinput-to-output speed increases with increased fixed gear operation dueto decreased gear ratios in the planetary gears 24, 26, and 28. Therotational speeds of the first and second electric machines 56 and 72,N_(A) and N_(B) respectively, are dependent on internal rotation of themechanism as defined by the clutching and are proportional to the inputspeed measured at the input shaft 12.

In response to operator input via the accelerator pedal 113 and brakepedal 112 as captured by the user interface 13, the HCP 5 and one ormore of the other control modules determine torque commands to controlthe torque generative devices comprising the engine 14 and first andsecond electric machines 56 and 72 to meet the operator torque requestat the output member 64 and transferred to the driveline 90. Based uponinput signals from the user interface 13 and the hybrid powertrainincluding the ESD 74, the HCP 5 determines the operator torque request,a commanded output torque between the transmission 10 and the driveline90, an input torque from the engine 14, clutch torques for thetorque-transfer clutches C1 70, C2 62, C3 73, C4 75 of the transmission10; and the motor torques for the first and second electric machines 56and 72, respectively, as is described hereinbelow. The commanded outputtorque can be a tractive torque wherein torque flow originates in theengine 14 and the first and second electric machines 56 and 72 and istransferred through the transmission 10 to the driveline 90, and can bea reactive torque wherein torque flow originates in the vehicle wheels93 of the driveline 90 and is transferred through the transmission 10 tofirst and second electric machines 56 and 72 and the engine 14.

Final vehicle acceleration can be affected by other factors including,e.g., road load, road grade, and vehicle mass. The operating range stateis determined for the transmission 10 based upon a variety of operatingcharacteristics of the hybrid powertrain. This includes the operatortorque request communicated through the accelerator pedal 113 and brakepedal 112 to the user interface 13 as previously described. Theoperating range state may be predicated on a hybrid powertrain torquedemand caused by a command to operate the first and second electricmachines 56 and 72 in an electrical energy generating mode or in atorque generating mode. The operating range state can be determined byan optimization algorithm or routine which determines optimum systemefficiency based upon operator demand for power, battery state ofcharge, and energy efficiencies of the engine 14 and the first andsecond electric machines 56 and 72. The control system manages torqueinputs from the engine 14 and the first and second electric machines 56and 72 based upon an outcome of the executed optimization routine, andsystem efficiencies are optimized thereby, to manage fuel economy andbattery charging. Furthermore, operation can be determined based upon afault in a component or system. The HCP 5 monitors the torque-generativedevices, and determines the power output from the transmission 10required in response to the desired output torque at output member 64 tomeet the operator torque request. As should be apparent from thedescription above, the ESD 74 and the first and second electric machines56 and 72 are electrically-operatively coupled for power flowtherebetween. Furthermore, the engine 14, the first and second electricmachines 56 and 72, and the electro-mechanical transmission 10 aremechanically-operatively coupled to transfer power therebetween togenerate a power flow to the output member 64.

Operation of the engine 14 and transmission 10 is constrained by power,torque and speed limits of the engine 14, the first and second electricmachines 56 and 72, the ESD 74 and the clutches C1 70, C2 62, C3 73, andC4 75. The operating constraints on the engine 14 and transmission 10can be translated to a set of system constraint equations executed asone or more algorithms in one of the control modules, e.g., the HCP 5.

Referring again to FIG. 1, in overall operation, the transmission 10operates in one of the operating range states through selectiveactuation of one or two of the torque-transfer clutches. Torqueconstraints for each of the engine 14 and the first and second electricmachines 56 and 72 and speed constraints for each of the engine 14, thefirst and second electric machines 56 and 72, and the output shaft 64 ofthe transmission 10 are determined. Battery power constraints for theESD 74 are determined, and are applied to further limit the motor torqueconstraints for the first and second electrical machines 56 and 72. Thepreferred operating region for the powertrain is determined using thesystem constraint equation, based upon the battery power constraints,the motor torque constraints, and the speed constraints. The preferredoperating region comprises a range of permissible operating torques orspeeds for the engine 14 and the first and second electric machines 56and 72.

By deriving and simultaneously solving dynamics equations of thetransmission 10, the torque limit, in this embodiment the output torqueT_(O), can be determined using the following linear equations:T _(M1) =T _(A)toT _(M1) *T _(A) +T _(B)toT _(M1) *T _(B)+Misc_(—) T_(M1)  [1]T _(M2) =T _(A)toT _(M2) *T _(A) +T _(B)toT _(M2) *T _(B)+Misc_(—) T_(M2)  [2]T _(M3) =T _(A)toT _(M3) *T _(A) +T _(B)toT _(M3) *T _(B)+Misc_(—) T_(M3)  [3]wherein, in this embodiment,

-   -   T_(M1) represents the output torque T_(O) at output member 64,    -   T_(M2) represents the input torque T_(I) at input shaft 12,    -   T_(M3) represents the reactive clutch torque(s) for the applied        torque-transfer clutches C1 70, C2 62, C3 73, C4 75 of the        transmission 10,    -   T_(A)toT_(M1), T_(A)toT_(M2), T_(A)toT_(M3) are contributing        factors of T_(A) to T_(M1), T_(M2), T_(M3), respectively,    -   T_(B)toT_(M1), T_(B)toT_(M2), T_(B)toT_(M3) are contributing        factors of T_(B) to T_(M1), T_(M2), T_(M3), respectively,    -   Misc_T_(M1), Misc_T_(M2), and Misc_T_(M3) are constants which        contribute to T_(M1), T_(M2), T_(M3) by N_(I) _(—) _(DOT), N_(O)        _(—) _(DOT), and N_(C) _(—) _(DOT) (time-rate changes in the        input speed, output speed and clutch slip speed) respectively,        and    -   T_(A) and T_(B) are the motor torques from the first and second        electric machines 56 and 72.        The torque parameters T_(M1), T_(M2), T_(M3) can be any three        independent parameters, depending upon the application.

The engine 14 and transmission 10 and the first and second electricmachines 56 and 72 have speed constraints, torque constraints, andbattery power constraints due to mechanical and system limitations.

The speed constraints can include engine speed constraints of N_(I)=0(engine off state), and N_(I) ranging from 600 rpm (idle) to 6000 rpmfor the engine 14. The speed constraints for the first and secondelectric machines 56 and 72 can be as follows:−10,500 rpm≦N_(A)≦+10,500 rpm, and−10,500 rpm≦N_(B)≦+10,500 rpm.

The torque constraints include engine torque constraints including T_(I)_(—) _(MIN)<T_(I)<T_(I) _(—) _(MAX), and motor torque constraints forthe first and second electric machines including T_(A) _(—)_(MIN)<T_(A)<T_(A) _(—) _(MAX) and T_(B) _(—) _(MIN)<T_(B)<T_(B) _(—)_(MAX). The motor torque constraints T_(A) _(—) _(MAX) and T_(A) _(—)_(MIN) comprise torque limits for the first electric machine 56 whenworking as a torque-generative motor and an electrical generator,respectively. The motor torque constraints T_(B) _(—) _(MAX) and T_(B)_(—) _(MIN) comprise torque limits for the second electric machine 72when working as a torque-generative motor and an electrical generator,respectively. The maximum and minimum motor torque constraints T_(A)_(—) _(MAX), T_(A) _(—) _(MIN), T_(B) _(—) _(MAX), T_(B) _(—) _(MIN) arepreferably obtained from data sets stored in tabular format within oneof the memory devices of one of the control modules. Such data sets areempirically derived from conventional dynamometer testing of thecombined motor and power electronics (e.g., power inverter) at varioustemperature and voltage conditions.

Battery power constraints comprise the available battery power withinthe range of P_(BAT) _(—) _(MIN) to P_(BAT) _(—) _(MAX), wherein P_(BAT)_(—) _(MIN) is maximum allowable battery charging power and P_(BAT) _(—)_(MAX) is the maximum allowable battery discharging power. Battery poweris defined as positive when discharging and negative when charging.

Minimum and maximum values for T_(M1) are determined within the speedconstraints, the motor torque constraints, clutch torque constraints,and the battery power constraints during ongoing operation, in order tocontrol operation of the engine 14, the first and second electricmachines 56 and 72, also referred to hereinafter as Motor A 56 and MotorB 72, and the transmission 10 to meet the operator torque request andthe commanded output torque.

An operating range, comprising a torque output range is determinablebased upon the battery power constraints of the ESD 74. Calculation ofbattery power usage, P_(BAT) is as follows:P _(BAT) =P _(A,ELEC) +P _(B,ELEC) +P _(DC) _(—) _(LOAD)  [4]wherein P_(A,ELEC) comprises electrical power from Motor A 56,

-   -   P_(B,ELEC) comprises electrical power from Motor B 72, and    -   P_(DC) _(—) _(LOAD) comprises known DC load, including accessory        loads.

Substituting equations for P_(A,ELEC) and P_(B,ELEC), yields thefollowing:P _(BAT)=(P _(A,MECH) +P _(A,LOSS))+(P _(B,MECH) +P _(B,LOSS))+P _(DC)_(—) _(LOAD)  [5]wherein P_(A,MECH) comprises mechanical power from Motor A 56,

-   -   P_(A,LOSS) comprises power losses from Motor A 56,    -   P_(B,MECH) comprises mechanical power from Motor B 72, and    -   P_(B,LOSS) comprises power losses from Motor B 72.

Eq. 5 can be restated as Eq. 6, below, wherein speeds, N_(A) and N_(B),and torques, T_(A) and T_(B), are substituted for powers P_(A) andP_(B). This includes an assumption that motor and inverter losses can bemathematically modeled as a quadratic equation based upon torque asfollows:

$\begin{matrix}{P_{BAT} = {\left( {{N_{A}T_{A}} + \left( {{{a_{1}\left( N_{A} \right)}T_{A}^{2}} + {{a_{2}\left( N_{A} \right)}T_{A}} + {a_{3}\left( N_{A} \right)}} \right)} \right) + \left( {{N_{B}T_{B}} + \left( {{{b_{1}\left( N_{B} \right)}T_{B}^{2}} + {{b_{2}\left( N_{B} \right)}T_{B}} + {b_{3}\left( N_{B} \right)}} \right)} \right) + P_{{DC}\_{LOAD}}}} & \lbrack 6\rbrack\end{matrix}$wherein N_(A), N_(B) comprise speeds of Motors A and B 56 and 72,

-   -   T_(A), T_(B) comprise torques of Motors A and B 56 and 72, and    -   a1, a2, a3, b1, b2, b3 each comprise quadratic coefficients        which are a function of respective motor speeds, N_(A), N_(B).

This can be restated as Eq. 7 as follows.

$\begin{matrix}{P_{BAT} = {{a_{1}*T_{A}^{2}} + {\left( {N_{A} + a_{2}} \right)*T_{A}} + {b_{1}*T_{B}^{2}} + {\left( {N_{B} + b_{2}} \right)*T_{B}} + {a\; 3} + {b\; 3} + P_{{DC}\_{LOAD}}}} & \lbrack 7\rbrack\end{matrix}$

This reduces to Eq. 8 as follows.

$\begin{matrix}{P_{BAT} = {{a_{1}\left\lbrack {T_{A}^{2} + {{T_{A}\left( {N_{A} + a_{2}} \right)}/a_{1}} + \left( {\left( {N_{A} + a_{2}} \right)/\left( {2*a_{1}} \right)} \right)^{2}} \right\rbrack} + {b_{1}\left\lbrack {T_{B}^{2} + {{T_{B}\left( {N_{B} + b_{2}} \right)}/b_{1}} + \left( {\left( {N_{B} + b_{2}} \right)/\left( {2*b_{1}} \right)} \right)^{2}} \right\rbrack} + {a\; 3} + {b\; 3} + P_{{DC}\_{LOAD}} - {\left( {N_{A} + a_{2}} \right)^{2}/\left( {4*a_{1}} \right)} - {\left( {N_{B} + b_{2}} \right)^{2}/\left( {4*b_{1}} \right)}}} & \lbrack 8\rbrack\end{matrix}$

This reduces to Eq. 9 as follows.

$\begin{matrix}{P_{BAT} = {{a_{1}\left\lbrack {T_{A} + {\left( {N_{A} + a_{2}} \right)/\left( {2*a_{1}} \right)}} \right\rbrack}^{2} + {b_{1}\left\lbrack {T_{B} + {\left( {N_{B} + b_{2}} \right)/\left( {2*b_{1}} \right)}} \right\rbrack}^{2} + a_{3} + b_{3} + P_{{DC}\_{LOAD}} - {\left( {N_{A} + a_{2}} \right)^{2}/\left( {4*a_{1}} \right)} - {\left( {N_{B} + b_{2}} \right)^{2}/\left( {4*b_{1}} \right)}}} & \lbrack 9\rbrack\end{matrix}$

This reduces to Eq. 10 as follows.

$\begin{matrix}{P_{BAT} = {\left\lbrack {{{{SQRT}\left( a_{1} \right)}*T_{A}} + {\left( {N_{A} + a_{2}} \right)/\left( {2*{{SQRT}\left( a_{1} \right)}} \right)}} \right\rbrack^{2} + {\left. \quad{\left\lbrack {{{{SQRT}\left( b_{1} \right)}*T_{B}} + N_{B} + b_{2}} \right)/\left( {2*{{SQRT}\left( b_{1} \right)}} \right)} \right\rbrack 2} + a_{3} + b_{3} + P_{{DC}\_{LOAD}} - {\left( {N_{A} + a_{2}} \right)^{2}/\left( {4*a_{1}} \right)} - {\left( {N_{B} + b_{2}} \right)^{2}/\left( {4*b_{1}} \right)}}} & \lbrack 10\rbrack\end{matrix}$

This reduces to Eq. 11 as follows.P _(BAT)=(A ₁ *T _(A) +A ₂)²+(B ₁ *T _(B) +B ₂)² +C  [11]wherein A₁=SQRT(a₁),

-   -   B₁=SQRT(b₁),    -   A₂=(N_(A)+a₂)/(2*SQRT(a₁)),    -   B₂=(N_(B)+b₂)/(2*SQRT(b₁)), and    -   C=a₃+b₃+P_(DC) _(—)        _(LOAD)−(N_(A)+a₂)²/(4*a₁)−(N_(B)+b₂)²/(4*b₁)

The motor torques T_(A) and T_(B) can be transformed to T_(X) and T_(Y)as follows:

$\begin{matrix}{\begin{bmatrix}T_{X} \\T_{Y}\end{bmatrix} = {{\begin{bmatrix}A_{1} & 0 \\0 & B_{1}\end{bmatrix}*\begin{bmatrix}T_{A} \\T_{B}\end{bmatrix}} + \begin{bmatrix}A_{2} \\B_{2}\end{bmatrix}}} & \lbrack 12\rbrack\end{matrix}$wherein T_(X) is the transformation of T_(A),

-   -   T_(Y) is the transformation of T_(B), and    -   A₁, A₂, B₁, B₂ comprise application-specific scalar values.

Eq. 11 can thus be further reduced as follows.P _(BAT)=(T _(X) ² +T _(Y) ²)+C  [13]P _(BAT) =R ² +C  [14]

Eq. 12 specifies the transformation of motor torque T_(A) to T_(X) andthe transformation of motor torque T_(B) to T_(Y). Thus, a newcoordinate system referred to as T_(X)/T_(Y) space is defined, and Eq.13 comprises battery power, P_(BAT), transformed into T_(X)/T_(Y) space.Therefore, the battery power range between maximum and minimum batterypower P_(BAT) _(—) _(MAX) and P_(BAT) _(—) _(MIN) can be calculated andgraphed as radii R_(Max) and R_(Min) with a center at locus (0, 0) inthe transformed space T_(X)/T_(Y), designated by the letter K as shownwith reference to FIG. 3, wherein:R _(Min) =SQRT(P _(BAT) _(—) _(MIN) −C), andR _(Max) =SQRT(P _(BAT) _(—) _(MAX) −C).

The minimum and maximum battery powers, P_(BAT) _(—) _(MIN) and P_(BAT)_(—) _(MAX), are preferably correlated to battery physics, e.g. state ofcharge, temperature, voltage and usage (amp-hour/hour). The parameter C,above, is defined as the absolute minimum possible battery power atgiven motor speeds, N_(A) and N_(B), within the motor torque limits.Physically, when T_(A)=0 and T_(B)=0 the output power from the first andsecond electric machines 56 and 72 is zero. Physically T_(X)=0 andT_(Y)=0 corresponds to a maximum charging power for the ESD 74. Thepositive sign (‘+’) is defined as discharging power from the ESD 74, andthe negative sign (‘−’) is defined as charging power into the ESD 74.R_(Max) defines a maximum battery power, typically a discharging power,and R_(Min) defines a maximum battery charging power.

The forgoing transformations to the T_(X)/T_(Y) space are shown in FIG.3, with representations of the battery power constraints as concentriccircles having radii of R_(Min) and R_(Max) (‘Battery PowerConstraints’) and linear representations of the motor torque constraints(‘Motor Torque Constraints’) circumscribing an allowable operatingregion. Analytically, the transformed vector [T_(X) T_(Y)] determined inEq. 12 is solved simultaneously with the vector defined in Eq. 13comprising the minimum and maximum battery powers identified by R_(Min)and R_(Max) to identify a range of allowable torques in the T_(X)/T_(Y)space which are made up of motor torques T_(A) and T_(B) constrained bythe minimum and maximum battery powers P_(BAT) _(—) _(MIN) to P_(BAT)_(—) _(MAX). The range of allowable torques in the T_(X)/T_(Y) space isshown with reference to FIG. 3, wherein points A, B, C, D, and Erepresent the bounds, and lines and radii are defined.

A constant torque line can be defined in the T_(X)/T_(Y) space, anddepicted in FIG. 3 (‘T_(M1)=C1’), comprising the limit torque T_(M1),described in Eq. 1, above. The limit torque T_(M1) comprises the outputtorque T_(O) in this embodiment, Eqs. 1, 2, and 3 restated in theT_(X)/T_(Y) space are as follows.T _(M1) =T _(A)toT _(M1)*(T _(X) −A ₂)/A ₁ +T _(B)toT _(M1)*(T _(Y) −B₂)/B ₁+Misc_(—) T _(M1)  [15]T _(M2) =T _(A)toT _(M2)*(T _(X) −A ₂)/A ₁ +T _(B)toT _(M2)*(T _(Y) −B₂)/B ₁+Misc_(—) T _(M2)  [16]T _(M3) =T _(A)toT _(M3)*(T _(X) −A ₂)/A ₁ +T _(B)toT _(M3)*(T _(Y) −B₂)/B ₁+Misc_(—) T _(M3)  [17]

Defining T_(M1) _(—) _(XY), T_(M2) _(—) _(XY), and T_(M3) _(—) _(XY) asparts of T_(M1), T_(M2), and T_(M3,) contributed by T_(A) and T_(B)only, then:T _(M1) _(—) _(XY) =T _(A)toT _(M1)*(T _(X) −A ₂)/A ₁ +T _(B)toT_(M1)*(T _(Y) −B ₂)/B ₁  [18]T _(M2) _(—) _(XY) =T _(A)toT _(M2)*(T _(X) −A ₂)/A ₁ +T _(B)toT_(M2)*(T _(Y) −B ₂)/B ₁  [19]T _(M3) _(—) _(XY) =T _(A)toT _(M3)*(T _(X) −A ₂)/A ₁ +T _(B)toT_(M3)*(T _(Y) −B ₂)/B ₁   [20]

The following coefficients can be defined:

-   T_(X)toT_(M1)=T_(A)toT_(M1)/A₁,-   T_(Y)toT_(M1)=T_(B)toT_(M1)/B₁,-   T_(M1) _(—) Intercept=T_(A)toT_(M1)*A₂/A₁+T_(B)toT_(M1)*B₂/B₁,-   T_(X)toT_(M2)=T_(A)toT_(M2)/A₁,-   T_(Y)toT_(M2)=T_(B)toT_(M2)/B₁,-   T_(M2) _(—) Intercept=T_(A)toT_(M2)*A₂/A₁+T_(B)toT_(M2)*B₂/B₁,-   T_(X)toT_(M3)=T_(A)toT_(M3)/A₁,-   T_(Y)toT_(M3)=T_(B)toT_(M3)/B₁, and-   T_(M3) _(—) Intercept=T_(A)toT_(M3)*A₂/A₁+T_(B)toT_(M3)*B₂/B₁.

Thus, Eqs. 1, 2, and 3 are transformed to T_(X)/T_(Y) space as follows.T _(M1) _(—) _(XY) =T _(X)toT _(M1) *T _(X) +T _(Y)toT _(M1) *T _(Y) +T_(M1) _(—) Intercept  [21]T _(M2) _(—) _(XY) =T _(X)toT _(M2) *T _(X) +T _(Y)toT _(M2) *T _(Y) +T_(M2) _(—) Intercept  [22]T _(M3) _(—) _(XY) =T _(X)toT _(M3) *T _(X) +T _(Y)toT _(M3) *T _(Y) +T_(M3) _(—) Intercept  [23]

The speed constraints, motor torque constraints, and battery powerconstraints can be determined during ongoing operation and expressed inlinear equations which are transformed to T_(X)/T_(Y) space. Eq. 21comprises a limit torque function describing the output torqueconstraint T_(M1), e.g., T_(O).

The torque limit of the transmission 10, in this embodiment the outputtorque T_(O), can be determined by using Eq. 21 subject to the T_(M2)and T_(M3) constraints defined by Eqs. 22 and 23 to determine atransformed maximum or minimum limit torque in the T_(X)/T_(Y) space,comprising one of T_(M1) _(—) _(XY)Max and T_(M1) _(—) _(XY)Min, e.g.,maximum and minimum output torques T_(O) _(—) _(Max) and T_(O) _(—)_(Min) that have been transformed. Subsequently the transformed maximumor minimum limit torque in the T_(X)/T_(Y) space can be retransformedout of the T_(X)/T_(Y) space to determine maximum or minimum limittorques T_(M1) _(—) Max and T _(M1) _(—) Min for managing control andoperation of the transmission 14 and the first and second electricmachines 56 and 72.

FIG. 4 shows motor torque constraints comprising the minimum and maximummotor torques for T_(A) and T_(B) transformed to T_(X)/T_(Y) space(‘Tx_Min’, ‘Tx_Max’, ‘Ty_Min’, ‘Ty_Max’). Battery power constraints aretransformed to the T_(X)/T_(Y) space (‘R_Min’, ‘R_Max’) and have acenter locus point K comprising (Kx, Ky)=(0,0). The output torqueconstraint (Tm1=−Tx+Ty) is shown, having a tangent point with thebattery power constraint.

Constraints comprising maximum and minimum limits for a first torqueinput to the transmission 10 are depicted (‘Tm2=Tm2_High_Lmt’ and‘Tm2=Tm2_Low_Lmt’), and preferably comprise the range of input torquesT_(I) at input shaft 12 transformed to T_(X)/T_(Y) space in thisembodiment and can be mathematically represented by the line T_(M2) _(—)_(XY) described with reference to Eq. 22, above. The lines T_(M2) _(—)_(XY) described in Eq. 22 include the T_(M2) _(—) Intercept having twodifferent values corresponding to the maximum limit and the minimumlimit for the engine input torque T_(I). Alternatively, the second inputtorque T_(M2) _(—) _(XY) can comprise a range of clutch torques oranother torque input.

Constraints comprising maximum and minimum limits for a second torqueinput to the transmission 10 are depicted (‘Tm3_High_Lmt’) and a lowlimit (‘Tm3_Low_Lmt’), and preferably comprise the range of appliedclutch torques transformed to T_(X)/T_(Y) space in this embodiment andcan be mathematically represented by the line T_(M3) _(—) _(XY)described with reference to Eq. 23, above. The lines T_(M3) _(—) _(XY)described in Eq. 23 include the T_(M3) _(—) Intercept having twodifferent values corresponding to the maximum limit and the minimumlimit for the applied one of the torque-transfer clutches C1 70, C2 62,C3 73, C4 75 of the transmission 10. Alternatively, the second inputtorque T_(M2) _(—) _(XY) can comprise a range of engine input torque oranother torque input.

The output torque line (‘Tm1=−Tx+Ty’) representing line T_(M1) _(—)_(XY) has a positive slope of a/b of the general form in Eq. 24:Tm1=a*Tx+b*Ty+C  [24]wherein a<0 and b>0 and C is a constant term. In the ensuingdescriptions, the line T_(M1) _(—) _(XY) has a positive slope of 1:1 forpurposes of illustration. The x-intercept C of Eq. 24 can change. Theoutput torque line comprises the limit torque function describing theoutput torque.

FIG. 5 (including 5A and 5B) depicts a process for determining one ofthe maximum and minimum output torques T_(O) _(—) _(Max) and T_(O) _(—)_(Min) based upon the speed constraints, motor torque constraints, andbattery power constraints, and the first torque input range and thesecond torque input range, with reference back to FIG. 4. Equations forthe maximum and minimum output torques, the speed constraints, the motortorque constraints, the battery power constraints, and the first torqueinput range and the second torque input range are transformed intoT_(X)/T_(Y) space. The maximum and minimum output torques T_(O) _(—)_(MAX) and T_(O) _(—) _(MIN) comprise one of T_(M1) _(—) _(XY)Max andT_(M1) _(—) _(XY)Min. It is determined whether the preferred solution isa maximum value for the output torque, i.e., T_(M1) _(—) _(XY)Max asindicated by setting a flag (‘Tm1_Max_Flag’), or alternatively whetherthe preferred solution is a minimum value for the output torque, i.e.,T_(M1) _(—) _(XY)Min as indicated by not setting the Tm1_Max_Flag flag.A maximum (or minimum) value for the output torque Tm1 is calculatedbased upon the motor torque constraints and battery power constraints inT_(X)/T_(Y) space, comprising one of T_(M1) _(—) _(XY)Max and T_(M1)_(—) _(XY)Min, and having coordinates of (Tx, Ty) (505).

A value for the second input torque T_(M2) _(—) _(XY) (‘Tm2_Value’) iscalculated at the maximum (or minimum) value for the output torque Tm1and having coordinates of (Tx, Ty), using Eq. 22 (530). It is determinedwhether the calculated value for the second input torque T_(M2) _(—)_(XY) (‘Tm2_Value’) is within the operating range of the second inputtorque, shown in FIG. 4 as the lines representing the maximum andminimum limits for the first torque input to the transmission 10(‘Tm2=Tm2_High_Lmt’ and ‘Tm2=Tm2_Low_Lmt’) (532).

When it is determined that the calculated value for the second inputtorque T_(M2) _(—) _(XY) (‘Tm2_Value’) is within the operating range ofthe second input torque at the maximum (or minimum) value for the firsttorque Tm1, an initially achievable first torque point havingcoordinates of (Tx1, Ty1) is set equal to (Tx, Ty) (536, 540). When itis determined that the calculated value for the second input torqueT_(M2) _(—) _(XY) (‘Tm2_Value’) is outside the operating range of thesecond input torque at the maximum (or minimum) value for the outputtorque Tm1, the (Tx, Ty) point is modified to an initially achievablefirst torque point having coordinates of (Tx1, Ty1) (534, 538). Theinitially achievable first torque point lies on one of the linesrepresenting the maximum and minimum limits for the first torque inputto the transmission 10, depending on the calculated value for the secondinput torque T_(M2) _(—) _(XY) at (Tx, Ty). In either instance, amaximum (or minimum) value for the output torque Tm1 is calculated atthe initially achievable first torque point having the coordinates of(Tx1, Ty1) using Eq. 21 (542).

A value for the third input torque T_(M3) _(—) _(XY) (‘Tm3_Value’) iscalculated at the maximum (or minimum) value for the first torque Tm1and having coordinates of (Tx, Ty), using Eq. 23 (510). It is determinedwhether the calculated value for the third input torque T_(M3) _(—)_(XY) (‘Tm3_Value’) is within the operating range of the third inputtorque, shown in FIG. 4 as the lines representing the high limit(‘Tm3_High_Lmt’) and the low limit (‘Tm3_Low_Lmt’) (512). When it isdetermined that the calculated value for the third input torque T_(M3)_(—) _(XY) (‘Tm3_Value’) is within the operating range of the thirdinput torque at the maximum (or minimum) value for the output torqueTm1, an initially achievable second torque point having coordinates of(Tx2, Ty2) is set equal to (Tx, Ty) (516, 520). When it is determinedthat the calculated value for the third input torque T_(M3) _(—) _(XY)(‘Tm3_Value’) is outside the operating range of the third input torqueat the maximum (or minimum) value for the output torque Tm1, the (Tx,Ty) point is modified to an initially achievable second torque pointhaving coordinates of (Tx2, Ty2) (514, 518). The initially achievablefirst torque point lies on one of the lines representing the maximum andminimum limits for the second torque input to the transmission 10,depending on the calculated value for the third input torque T_(M3) _(—)_(XY) at (Tx, Ty). In either instance, a maximum (or minimum) value forthe output torque Tm1 is calculated at the initially achievable secondtorque point having the coordinates of (Tx2, Ty2) using Eq. 21 (522).

The initially achievable first torque point having the coordinates of(Tx1, Ty1) and the initially achievable second torque point having thecoordinates of (Tx2, Ty2) are compared (550). When the preferredsolution is a maximum value for the output torque, i.e., T_(M1) _(—)_(XY)Max as indicated by setting the flag (‘Tm1_Max_Flag’) and theinitially achievable first torque point having the coordinates of (Tx1,Ty1) is greater than or equal to the initially achievable second torquepoint having the coordinates of (Tx2, Ty2), then the final solution(Tx_Final, Ty_Final) is the output torque at the achievable first torquepoint having the coordinates of (Tx1, Ty1) (550, 570).

When the preferred solution is a maximum value for the output torque,i.e., T_(M1) _(—) _(XY)Max as indicated by setting the flag(‘Tm1_Max_Flag’) and the initially achievable first torque point havingthe coordinates of (Tx1, Ty1) is less than the initially achievablesecond torque point having the coordinates of (Tx2, Ty2), then the finalsolution (Tx_Final, Ty_Final) is the output torque at the achievablesecond torque point having the coordinates of (Tx2, Ty2) (550, 560).

When the preferred solution is a minimum value for the output torque,i.e., T_(M1) _(—) _(XY)Min as indicated by not setting the flag(‘Tm1_Max_Flag’) and the initially achievable first torque point havingthe coordinates of (Tx1, Ty1) is less than or equal to the initiallyachievable second torque point having the coordinates of (Tx2, Ty2),then the final solution (Tx_Final, Ty_Final) is the achievable firsttorque point having the coordinates of (Tx1, Ty1) (550, 570). When thepreferred solution is a minimum value for the output torque, i.e.,T_(M1) _(—) _(XY)Min as indicated by not setting the flag(‘Tm1_Max_Flag’) and the initially achievable first torque point havingthe coordinates of (Tx1, Ty1) is greater than the initially achievablesecond torque point having the coordinates of (Tx2, Ty2), then the finalsolution (Tx_Final, Ty_Final) is the output torque at the achievablesecond torque point having the coordinates of (Tx2, Ty2) (550, 560).

The (Tx_Final, Ty_Final) point represents the preferred solution forcontrolling operation that can be retransformed to motor torques (T_(A),T_(B)) to control operation of the first and second electric machines 56and 72 to achieve the output torque (580). Thus, the preferred minimumor maximum output torque is constrained based upon the speedconstraints, the motor torque constraints, the battery powerconstraints, and the first torque input range, e.g., the input torqueT_(I), and the second torque input range, e.g., the clutch torque.

The embodiment described hereinabove is based upon the output torqueline T_(M1) _(—) _(XY) having a positive slope of a/b of the generalform in Eq. 24 (as above):Tm1=a*Tx+b*Ty+C  [24]wherein a<0 and b>0 and C is a constant term, with a slope of a/b=1:1for purposes of illustration with the x-intercept C being changeable,and is indicative of a maximum battery power discharge. The descriptionis applicable to combinations of a>0, b<0, and the slope of a/b beingless than 1:1 and being greater than 1:1.

The disclosure has described certain preferred embodiments andmodifications thereto. Further modifications and alterations may occurto others upon reading and understanding the specification. Therefore,it is intended that the disclosure not be limited to the particularembodiment(s) disclosed as the best mode contemplated for carrying outthis disclosure, but that the disclosure will include all embodimentsfalling within the scope of the appended claims.

The invention claimed is:
 1. A method for controlling anelectro-mechanical transmission operatively coupled to first and secondelectric machines to transmit power to an output member, the methodcomprising: determining motor torque constraints for the first andsecond electric machines; determining battery power constraints for anelectrical energy storage device electrically connected to the first andsecond electric machines; determining a range for a first torque inputto the electro-mechanical transmission; determining a range for a secondtorque input to the electro-mechanical transmission; determining apreferred output torque to the output member of the electro-mechanicaltransmission that is achievable within the motor torque constraints, isachievable within the range for the first torque input, is achievablewithin the range for the second torque input, and is based upon thebattery power constraints; and controlling operation of theelectro-mechanical transmission and the first and second electricmachines to achieve the preferred output torque to the output member ofthe electro-mechanical transmission; wherein determining the preferredoutput torque comprises: formulating mathematical equations representingthe motor torque constraints comprising maximum and minimum motor torqueconstraints for the first and second electric machines; formulatingmathematical equations representing maximum and minimum battery powerconstraints; formulating a mathematical equation representing the outputtorque; formulating mathematical equations representing the range forthe first torque input; formulating mathematical equations representingthe range for the second torque input; transforming the mathematicalequations representing the maximum and minimum battery power constraintsto equations of concentric circles having respective radii; transformingthe mathematical equations representing the maximum and minimum motortorque constraints for the first and second electric machines toequations comprising lines; transforming the mathematical equationsrepresenting the range for the first torque input to equationscomprising lines; transforming the mathematical equations representingthe range for the second torque input to equations comprising lines;transforming the mathematical equation representing the output torque toan equation comprising a line; determining at least one transformedachievable output torque based upon the transformed mathematicalequations representing the maximum and minimum motor torque constraintsfor the first and second electric machines, the maximum and minimumbattery power constraints, the range for the first torque input and therange for the second torque input; determining a transformed achievablemaximum output torque corresponding to the at least one transformedachievable output torque; and retransforming the transformed achievablemaximum output torque as the preferred output torque to the outputmember.
 2. The method of claim 1, wherein the preferred output torquecomprises a maximum tractive torque to the output member.
 3. The methodof claim 1, wherein the preferred output torque comprises a maximumbraking torque to the output member.
 4. The method of claim 1, whereinthe first torque input comprises an engine input torque.
 5. The methodof claim 4, wherein the second torque input comprises a torque for anapplied clutch.
 6. The method of claim 1, wherein controlling operationof the electro-mechanical transmission and the first and second electricmachines to achieve the preferred output torque to the output member ofthe electro-mechanical transmission comprises controlling operation ofthe electro-mechanical transmission and the first and second electricmachines to achieve the preferred output torque at the output memberthat is achievable within the motor torque constraints, is achievablewithin the range for the first torque input, is achievable within therange for the second torque input, and is based upon the battery powerconstraints.
 7. The method of claim 1, wherein the preferred outputtorque comprises a commanded output torque to the output member toachieve an operator torque request.
 8. The method of claim 1, whereinthe battery power constraint comprises a maximum battery dischargingpower and a maximum battery charging power.
 9. The method of claim 1,further comprising: determining an initially achievable first torquepoint achievable within the motor torque constraints, achievable withinthe range for the first torque input, and based upon the battery powerconstraints; determining an initially achievable second torque pointachievable within the motor torque constraints, achievable within therange for the second torque input, and based upon the battery powerconstraints; and selecting the preferred output torque to the outputmember based upon the initially achievable first torque point and theinitially achievable second torque point.
 10. The method of claim 1,further comprising: using the transformed achievable maximum outputtorque to determine preferred motor torques for the first and secondelectric machines.
 11. The method of claim 1, wherein determining thetransformed achievable maximum output torque corresponding to the atleast one transformed achievable output torque comprises calculating atleast one intersection of the transformed mathematical equationsrepresenting the maximum and minimum battery power constraints, thetransformed mathematical equations representing the maximum and minimummotor torque constraints for the first and second electric machines, thetransformed mathematical equation representing the first and secondtorque inputs, and the transformed mathematical equation representingthe output torque.
 12. A method for controlling an electro-mechanicaltransmission operatively coupled to first and second electric machinesto transmit mechanical power to an output member, the method comprising:determining motor torque constraints for the first and second electricmachines; determining battery power constraints for an electrical energystorage device electrically connected to the first and second electricmachines; determining a range for a first torque input to theelectro-mechanical transmission; determining a range for a second torqueinput to the electro-mechanical transmission; formulating mathematicalequations representing the motor torque constraints for the first andsecond electric machines, the battery power constraints, the outputtorque, the range for the first torque input, and the range for thesecond torque input; transforming the mathematical equationsrepresenting the battery power constraints to equations of concentriccircles having respective radii and transforming the mathematicalequations representing the motor torque constraints for the first andsecond electric machines, the output torque, the range for the firsttorque input, and the range for the second torque input to equationscomprising lines; simultaneously solving the said transformedmathematical equations to determine at least one transformed achievableoutput torque; and retransforming the transformed achievable outputtorque to determine a preferred output torque to the output member ofthe electro-mechanical transmission that is achievable within the motortorque constraints, is achievable within the range for the first torqueinput, is achievable within the range for the second torque input, andis based upon the battery power constraints.